The th
complex Fourier coefficient of a periodic function
of period
is
The Fourier coefficients are expansion coefficients in the corresponding Fourier series of .
In the Wolfram Language, the complex Fourier coefficient is implemented as FourierCoefficient[expr, t, n]. For the real trigonometric form, the cosine and sine coefficients are implemented as FourierCosCoefficient[expr, t, n] and FourierSinCoefficient[expr, t, n], respectively.